{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 插值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "拉格朗日插值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lagrange_interpolate(points: list, simplify_result=True, verbose=False):\n",
    "    \"\"\"拉格朗日插值\n",
    "\n",
    "    Args:\n",
    "        points: list, [(x1, y1), (x2, y2), ..., (xn, yn)]\n",
    "        simplify_result: bool, 化简最终结果, default True\n",
    "        verbose: bool, 输出每一步的结果, default False\n",
    "\n",
    "    Returns: \n",
    "        L: sympy object of Symbol('x'), 插值多项式 $L(x)$\n",
    "    \"\"\"\n",
    "    x = Symbol('x')\n",
    "    L = 0  # 插值多项式\n",
    "    for i, point in enumerate(points):\n",
    "        xi, yi = point\n",
    "        li = 1\n",
    "        for j in range(len(points)):\n",
    "            if j == i:\n",
    "                continue\n",
    "            xj, yj = points[j]\n",
    "            li *= (x - xj) / (xi - xj)\n",
    "        L += yi * li\n",
    "        if verbose:\n",
    "            print(f\"l_{i}(x) = \", simplify(expand(yi * li)))\n",
    "        \n",
    "    if simplify_result:\n",
    "        L = simplify(L)\n",
    "    return L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "插值多项式: -3.20000000000042e-5*x**2 + 0.0178390000000004*x - 0.00154799999999966\n",
      "Hypothesis:   0.199368500000004\n",
      "Actual vaule: 0.199367934417197\n"
     ]
    }
   ],
   "source": [
    "points = [(11, 0.190809), (12, 0.207912), (13, 0.224951)]\n",
    "\n",
    "L = lagrange_interpolate(points)\n",
    "print('插值多项式:', L)\n",
    "print('Hypothesis:  ', L.subs(Symbol('x'), 11.5))\n",
    "print('Actual vaule:', sin(rad(11.5)).evalf())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "牛顿插值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 差商缓存\n",
    "__difference_quotient_cache = {}\n",
    "\n",
    "def difference_quotient(f, xs: list, verbose=False):\n",
    "    \"\"\"求差商 $f[xs...]$\n",
    "    \n",
    "    Args:\n",
    "        f: function, 函数\n",
    "        xs: list, 要计算的差商的 $f[x0, x1, ...]$ 的参数值：[x0, x1, ...]\n",
    "        verbose: bool, 打印出每一步计算差商的值, default False\n",
    "\n",
    "    Returns:\n",
    "        dq: sympy object, 差商值\n",
    "    \"\"\"\n",
    "\n",
    "    # 尝试从缓存读取\n",
    "    __key = str([(x, f(x)) for x in xs])\n",
    "    if __key in __difference_quotient_cache:\n",
    "        if verbose:\n",
    "            print(f\"cached: f{xs}: {__difference_quotient_cache[__key]}\")\n",
    "        return __difference_quotient_cache[__key]\n",
    "\n",
    "    if len(xs) == 1: # 0阶\n",
    "        dq = sympify(f(xs[0]))\n",
    "    else: # n 阶\n",
    "        dq_h = difference_quotient(f, xs[:-1], verbose)\n",
    "        dq_l = difference_quotient(f, xs[1: ], verbose)\n",
    "        dq = (dq_l - dq_h) / (xs[-1] - xs[0])\n",
    "    \n",
    "    if verbose:\n",
    "        print(f\"f{xs}: {dq}\")\n",
    "\n",
    "    # 写入缓存\n",
    "    __difference_quotient_cache[__key] = dq\n",
    "\n",
    "    return dq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def newton_interpolate(points: list, N_start=0, points_start=[], simplify_result=True, verbose=False):\n",
    "    \"\"\"牛顿插值\n",
    "\n",
    "    Args:\n",
    "        points: [(x1, y1), (x2, y2), ..., (xn, yn)]： 插值点\n",
    "\n",
    "        N_start: a sympy object of Symbol('x'), 起始插值多项式。\n",
    "        points_start: [(x1, y1), (x2, y2), ..., (xn, yn)]: 计算 N_start 用的插值点\n",
    "                 该函数中做的插值会「承袭」这个用 points_start 计算的 N_start，在其基础上用新增插值点 points 去改进。\n",
    "                 default 0 (从头开始构建).\n",
    "\n",
    "        simplify_result: bool, 化简最终结果, default True\n",
    "        verbose: 打印出每一步计算差商的值, default False\n",
    "\n",
    "    Returns: \n",
    "        N: a sympy object of Symbol('x'), 插值多项式 $N(x)$\n",
    "    \"\"\"\n",
    "    x = Symbol('x')\n",
    "    \n",
    "    # sympify points\n",
    "    # for i in range(len(points)):\n",
    "    #     points[i] = sympify(points[i][0]), sympify(points[i][1])\n",
    "    \n",
    "    f = lambda x: dict(points + points_start)[x]\n",
    "    \n",
    "    xs = [p[0] for p in points_start] # 承袭的插值点\n",
    "    N = N_start   # 承袭的插值多项式\n",
    "    for point in points:\n",
    "        xs.append(point[0])\n",
    "        N += difference_quotient(f, xs, verbose) * prod([x - xi for xi in xs[:-1]])\n",
    "    \n",
    "    if simplify_result:\n",
    "        N = simplify(N)\n",
    "    return N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "插值多项式: -3.20000000000042e-5*x**2 + 0.0178390000000001*x - 0.00154800000000063\n",
      "Hypothesis:   0.199368500000000\n",
      "Actual vaule: 0.199367934417197\n",
      "承袭:\n",
      "cached: f[11, 12, 13]: -0.0000320000000000042\n",
      "cached: f[12, 13]: 0.0170390000000000\n",
      "cached: f[13]: 0.224951000000000\n",
      "f[11.2]: 0.194234351219972\n",
      "f[13, 11.2]: 0.0170648048777933\n",
      "f[12, 13, 11.2]: -0.0000322560972416778\n",
      "f[11, 12, 13, 11.2]: -0.00000128048620836791\n",
      "cached: f[11, 12, 13, 11.2]: -0.00000128048620836791\n",
      "cached: f[12, 13, 11.2]: -0.0000322560972416778\n",
      "cached: f[13, 11.2]: 0.0170648048777933\n",
      "cached: f[11.2]: 0.194234351219972\n",
      "f[11.7]: 0.202787295356512\n",
      "f[11.2, 11.7]: 0.0171058882730810\n",
      "f[13, 11.2, 11.7]: -0.0000316026117597499\n",
      "f[12, 13, 11.2, 11.7]: -0.00000217828493975971\n",
      "f[11, 12, 13, 11.2, 11.7]: -0.00000128256961627400\n",
      "插值多项式: -1.282569616274e-6*x**4 + 5.9256799679765e-5*x**3 - 0.00105582207039453*x**2 + 0.0256792199573976*x - 0.0240006476355346\n",
      "Hypothesis:   0.199367875528590\n",
      "Actual vaule: 0.199367934417197\n"
     ]
    }
   ],
   "source": [
    "points = [(11, 0.190809), (12, 0.207912), (13, 0.224951)]\n",
    "\n",
    "N = newton_interpolate(points)\n",
    "print('插值多项式:', N)\n",
    "print('Hypothesis:  ', N.subs(Symbol('x'), 11.5))\n",
    "print('Actual vaule:', sin(rad(11.5)).evalf())\n",
    "\n",
    "# 承袭之前的 N:\n",
    "print('承袭:')\n",
    "new_points = [(11.2, sin(rad(11.2)).evalf()), (11.7, sin(rad(11.7)).evalf())]\n",
    "N1 = newton_interpolate(new_points, N_start=N, points_start=points, verbose=True)\n",
    "print('插值多项式:', N1)\n",
    "print('Hypothesis:  ', N1.subs(Symbol('x'), 11.5).evalf())\n",
    "print('Actual vaule:', sin(rad(11.5)).evalf())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'[(11, 0.190809)]': 0.190809000000000,\n",
       " '[(12, 0.207912)]': 0.207912000000000,\n",
       " '[(11, 0.190809), (12, 0.207912)]': 0.0171030000000000,\n",
       " '[(13, 0.224951)]': 0.224951000000000,\n",
       " '[(12, 0.207912), (13, 0.224951)]': 0.0170390000000000,\n",
       " '[(11, 0.190809), (12, 0.207912), (13, 0.224951)]': -3.20000000000042e-5,\n",
       " '[(11.2, 0.194234351219972)]': 0.194234351219972,\n",
       " '[(13, 0.224951), (11.2, 0.194234351219972)]': 0.0170648048777933,\n",
       " '[(12, 0.207912), (13, 0.224951), (11.2, 0.194234351219972)]': -3.22560972416778e-5,\n",
       " '[(11, 0.190809), (12, 0.207912), (13, 0.224951), (11.2, 0.194234351219972)]': -1.28048620836791e-6,\n",
       " '[(11.7, 0.202787295356512)]': 0.202787295356512,\n",
       " '[(11.2, 0.194234351219972), (11.7, 0.202787295356512)]': 0.0171058882730810,\n",
       " '[(13, 0.224951), (11.2, 0.194234351219972), (11.7, 0.202787295356512)]': -3.16026117597499e-5,\n",
       " '[(12, 0.207912), (13, 0.224951), (11.2, 0.194234351219972), (11.7, 0.202787295356512)]': -2.17828493975971e-6,\n",
       " '[(11, 0.190809), (12, 0.207912), (13, 0.224951), (11.2, 0.194234351219972), (11.7, 0.202787295356512)]': -1.28256961627400e-6}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "__difference_quotient_cache"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "三弯矩法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def spline3_interpolate(points: list, simplify_result=True):\n",
    "    \"\"\"三弯矩法插值\n",
    "\n",
    "    三弯矩法进行三次样条插值。使用自由边界条件。\n",
    "\n",
    "    Args:\n",
    "        points: list, [(x1, y1), (x2, y2), ..., (xn, yn)]\n",
    "        simplify_result: bool, 化简最终结果, default True\n",
    "\n",
    "    Returns: \n",
    "        L: sympy Piecewise object of Symbol('x'), 插值多项式 $L(x)$\n",
    "    \"\"\"\n",
    "    # 排序给定的点\n",
    "    ps = sorted(points, key=lambda p: p[0])\n",
    "    n = len(points)\n",
    "\n",
    "    # points to a function\n",
    "    _f_dict = dict(ps)\n",
    "    def f(x):\n",
    "        return _f_dict[x]\n",
    "\n",
    "    # $h_k = x_{k+1} - x_k$\n",
    "    def h(k):\n",
    "        return ps[k+1][0] - ps[k][0]\n",
    "\n",
    "    hks = [h(0)]\n",
    "\n",
    "    # 用方程 D * M = d 解出 M\n",
    "\n",
    "    D = np.zeros((n, n))\n",
    "    d = np.zeros(n)\n",
    "\n",
    "    for k in range(1, n-1):\n",
    "        # $h_k$, $h_{k-1}$\n",
    "        hks.append(h(k))\n",
    "        hk, hks1 = hks[k], hks[k-1]\n",
    "\n",
    "        # $\\mu_k$ -> mu, $\\lambda_k$ -> ld\n",
    "        _fra = hks1 + hk\n",
    "        mu = hks1 / _fra\n",
    "        ld = hk / _fra\n",
    "\n",
    "        # $\\mu_kM_{k-1}+2M_k+\\lambda_kM_{k+1} = d_k$\n",
    "        D[k, k-1] = mu\n",
    "        D[k, k]   = 2\n",
    "        D[k, k+1] = ld\n",
    "        d[k] = 6 * difference_quotient(f, [ps[k-1][0], ps[k][0], ps[k+1][0]])\n",
    "\n",
    "    # 边界条件\n",
    "    # Natural Boundary\n",
    "    D[0, 0] = 1\n",
    "    D[n-1, n-1] = 1\n",
    "\n",
    "    d[0] = 0\n",
    "    d[n-1] = 0\n",
    "\n",
    "    # 解出 M\n",
    "    M = np.linalg.solve(D, d)\n",
    "\n",
    "    # 插值函数\n",
    "    piecewises = []\n",
    "    for k in range(n-1):\n",
    "        s  = M[k] * (ps[k+1][0] - _x) ** 3 / (6 * hks[k])\n",
    "        s += M[k+1] * (_x - ps[k][0]) ** 3 / (6 * hks[k])\n",
    "        s += (ps[k][1] - M[k] * hks[k]**2 / 6) * (ps[k+1][0] - _x) / hks[k]\n",
    "        s += (ps[k+1][1] - M[k+1] * hks[k]**2 / 6) * (_x - ps[k][0]) / hks[k]\n",
    "        if simplify_result:\n",
    "            s = simplify(s)\n",
    "        piecewises.append((s, And(_x >= ps[k][0], _x <= ps[k+1][0])))\n",
    "\n",
    "    return Piecewise(*piecewises)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "题目\n",
    "2．区间 $[-5, 5]$ 作等距划分：..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 1 / (1 + x ** 2)\n",
    "\n",
    "def get_points(s, n, f):\n",
    "    \"\"\"在闭区间 s 作 n 等距划分, 输出 n+1 个插值点 [(x0, f(x0)), (x1, f(x1)), ..., (xn, f(xn))]\n",
    "    e.g. \n",
    "        get_points([-5, 5], 2, lambda x: 1 / (1 + x ** 2))\n",
    "    output: [(-5.0, 0.038461538461538464), (0.0, 1.0), (5.0, 0.038461538461538464)]\n",
    "    \"\"\"\n",
    "    h = (s[1] - s[0]) / n\n",
    "    xs = [s[0] + k * h for k in range(n+1)]\n",
    "    points = [(x, f(x)) for x in xs]\n",
    "    return points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "多项式插值：\n",
      "n = 5:\t0.00192307692307692*x**4 - 0.0692307692307692*x**2 + 0.567307692307692\n",
      "n = 10:\t-2.26244343891403e-5*x**10 + 0.00126696832579186*x**8 + 8.67361737988404e-19*x**7 - 0.0244117647058824*x**6 - 6.93889390390723e-18*x**5 + 0.19737556561086*x**4 + 5.55111512312578e-17*x**3 - 0.67420814479638*x**2 + 2.4980018054066e-16*x + 1.0\n",
      "n = 20:\t2.72817068149796e-9*x**20 - 2.65314598775677e-7*x**18 + 2.11758236813575e-22*x**17 + 1.07425130797334e-5*x**16 - 0.000236412102809886*x**14 + 5.42101086242752e-20*x**13 + 0.00310184793200599*x**12 - 4.33680868994202e-19*x**11 - 0.0251135266738695*x**10 + 1.04083408558608e-17*x**9 + 0.126252909857124*x**8 - 4.16333634234434e-17*x**7 - 0.391630076762969*x**6 + 1.52655665885959e-16*x**5 + 0.753353962815113*x**4 - 8.32667268468867e-17*x**3 - 0.965739184991246*x**2 + 8.50014503228635e-17*x + 1.0\n",
      "\n",
      "三次样条插值：\n",
      "n = 5:\tPiecewise((-0.0242914979757085*x + 1.72064777327935*(0.2*x + 1)**3 - 0.0829959514170041, (x >= -5.0) & (x <= -3.0)), (-0.0265182186234818*x**3 - 0.156072874493927*x**2 - 0.0795546558704453*x + 0.55, (x >= -3.0) & (x <= -1.0)), (0.576518218623482 - 0.0765182186234818*x**2, (x >= -1.0) & (x <= 1.0)), (0.0265182186234818*x**3 - 0.156072874493927*x**2 + 0.0795546558704453*x + 0.55, (x >= 1.0) & (x <= 3.0)), (0.0242914979757085*x - 1.72064777327935*(0.2*x - 1)**3 - 0.0829959514170041, (x >= 3.0) & (x <= 5.0)))\n",
      "n = 10:\tPiecewise((0.0176283092922677*x + 0.341710207244819*(0.2*x + 1)**3 + 0.126603084922877, (x >= -5.0) & (x <= -4.0)), (0.00714607134821629*x**3 + 0.0939539011524711*x**2 + 0.434449138771531*x + 0.750706232344191, (x >= -4.0) & (x <= -3.0)), (0.00669108272293192*x**3 + 0.0898590035249119*x**2 + 0.422164445888853*x + 0.738421539461514, (x >= -3.0) & (x <= -2.0)), (0.107266068348291*x**3 + 0.693308917277068*x**2 + 1.62906427339317*x + 1.54302142446439, (x >= -2.0) & (x <= -1.0)), (-0.435755356116097*x**3 - 0.935755356116097*x**2 + 1.0, (x >= -1.0) & (x <= 0.0)), (0.435755356116097*x**3 - 0.935755356116097*x**2 + 1.0, (x >= 0.0) & (x <= 1.0)), (-0.107266068348291*x**3 + 0.693308917277068*x**2 - 1.62906427339317*x + 1.54302142446439, (x >= 1.0) & (x <= 2.0)), (-0.00669108272293192*x**3 + 0.0898590035249118*x**2 - 0.422164445888853*x + 0.738421539461513, (x >= 2.0) & (x <= 3.0)), (-0.00714607134821629*x**3 + 0.0939539011524711*x**2 - 0.434449138771531*x + 0.750706232344191, (x >= 3.0) & (x <= 4.0)), (-0.0176283092922677*x - 0.341710207244819*(0.2*x - 1)**3 + 0.126603084922877, (x >= 4.0) & (x <= 5.0)))\n",
      "n = 20:\tPiecewise((0.0159894257773933*x + 0.602572179176649*(0.2*x + 1)**3 + 0.118408667348505, (x >= -5.0) & (x <= -4.5)), (0.00123647934877117*x**3 + 0.0239233373585306*x**2 + 0.15979877464138*x + 0.39437990856215, (x >= -4.5) & (x <= -4.0)), (0.00396184120838417*x**3 + 0.0566276796738866*x**2 + 0.290616143902804*x + 0.568803067577382, (x >= -4.0) & (x <= -3.5)), (0.00688951874776995*x**3 + 0.0873682938374373*x**2 + 0.398208293475231*x + 0.694327242078547, (x >= -3.5) & (x <= -3.0)), (0.0126608790854682*x**3 + 0.139310536876722*x**2 + 0.554035022593086*x + 0.850153971196401, (x >= -3.0) & (x <= -2.5)), (0.0283485524184901*x**3 + 0.256968086874386*x**2 + 0.848178897587244*x + 1.09527386702487, (x >= -2.5) & (x <= -2.0)), (0.0458282003652398*x**3 + 0.361845974554884*x**2 + 1.05793467294824*x + 1.23511105059886, (x >= -2.0) & (x <= -1.5)), (0.100274985643097*x**3 + 0.606856508305243*x**2 + 1.42545047357378*x + 1.41886895091163, (x >= -1.5) & (x <= -1.0)), (-0.262312758322244*x**3 - 0.48090672359078*x**2 + 0.337687241677756*x + 1.05628120694629, (x >= -1.0) & (x <= -0.5)), (-0.712562413892585*x**3 - 1.15628120694629*x**2 - 2.22044604925031e-16*x + 1.0, (x >= -0.5) & (x <= 0.0)), (0.712562413892585*x**3 - 1.15628120694629*x**2 + 2.22044604925031e-16*x + 1.0, (x >= 0.0) & (x <= 0.5)), (0.262312758322244*x**3 - 0.480906723590781*x**2 - 0.337687241677756*x + 1.05628120694629, (x >= 0.5) & (x <= 1.0)), (-0.100274985643097*x**3 + 0.606856508305243*x**2 - 1.42545047357378*x + 1.41886895091163, (x >= 1.0) & (x <= 1.5)), (-0.0458282003652397*x**3 + 0.361845974554884*x**2 - 1.05793467294824*x + 1.23511105059886, (x >= 1.5) & (x <= 2.0)), (-0.0283485524184901*x**3 + 0.256968086874386*x**2 - 0.848178897587245*x + 1.09527386702487, (x >= 2.0) & (x <= 2.5)), (-0.0126608790854682*x**3 + 0.139310536876722*x**2 - 0.554035022593086*x + 0.850153971196401, (x >= 2.5) & (x <= 3.0)), (-0.00688951874776995*x**3 + 0.0873682938374373*x**2 - 0.398208293475231*x + 0.694327242078547, (x >= 3.0) & (x <= 3.5)), (-0.00396184120838416*x**3 + 0.0566276796738865*x**2 - 0.290616143902804*x + 0.568803067577381, (x >= 3.5) & (x <= 4.0)), (-0.00123647934877118*x**3 + 0.0239233373585307*x**2 - 0.15979877464138*x + 0.39437990856215, (x >= 4.0) & (x <= 4.5)), (-0.0159894257773933*x - 0.602572179176649*(0.2*x - 1)**3 + 0.118408667348505, (x >= 4.5) & (x <= 5.0)))\n"
     ]
    }
   ],
   "source": [
    "hps = {}  # 多项式插值\n",
    "hss = {}  # 三次样条插值\n",
    "for n in [5, 10, 20]:\n",
    "    ps = get_points([-5, 5], n, f)\n",
    "    # 多项式插值\n",
    "    # h = lagrange_interpolate(ps)\n",
    "    h = newton_interpolate(ps)\n",
    "    hps[n] = h\n",
    "\n",
    "    # 三次样条插值\n",
    "    s = spline3_interpolate(ps)\n",
    "    hss[n] = s\n",
    "\n",
    "print('多项式插值：')\n",
    "for k in hps:\n",
    "    print(f'n = {k}:\\t{hps[k]}')\n",
    "print('\\n三次样条插值：')\n",
    "for k in hss:\n",
    "    print(f'n = {k}:\\t{hss[k]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 画图\n",
    "def show_plot_range(r, hs, title):\n",
    "    \"\"\"画图比较插值结果\n",
    "    r：区间\n",
    "    hs: 插值结果组 {n: h(x)}\n",
    "    title: 图标题\n",
    "    \"\"\"\n",
    "    x = Symbol('x')\n",
    "    colors = (c for c in [0, 'b', 'g', 'r'])\n",
    "\n",
    "    plt = plot(f(x), (x, *r), show=False, line_color=next(colors), label='f(x)', legend=True, title=title)\n",
    "    for n in hs:\n",
    "        p = plot(hs[n], (x, *r), show=False, line_color=next(colors), label=f'n={n}', legend=True)\n",
    "        plt.extend(p)\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
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   ],
   "source": [
    "# 画图：多项式插值\n",
    "show_plot_range((-5, 5), hps, 'Polynomial Interpolation')\n",
    "show_plot_range((-5, -3), hps, 'Polynomial Interpolation')\n",
    "show_plot_range((-1, 1), hps, 'Polynomial Interpolation')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zuneUu3hRf1vP0bHg5x4eHhw5cqSSov1/UoMSQogaLCstHd3Jk1yIjsRn0GDemreYju070rt3b9LT0/PLZWfD5ctgbw+mpgYM+BZSgxJCiEpWyKwtZXLLrDAFZF5LxSgiHCOVS7StEdHRMQQHP4/vSl+GDBnC5s2bSUhIYO3atWRn65OUhQUYGelHnPj0008BiIqKon379tjY2PDOO+/wwAMPlO8BFEESlBBC1EDpySmYRp1FpykiHU1pnOGBm5sbvr6+APj5+REdHc2sWbN46aVXOHZM3/Z0+7NPjRs35vz589jb23Pw4EEGDhxIWFgYNjY2hey1fEmCEkKISlZUjae8pF1KwiImmixjRWQDE9wcm3Mx7iLm5ub5ZYyNjUlPT2fhwoWsWrWWrKz/rz3B/9egzM3N89fz8/PDw8ODM2fOVMrknJKghBCiBkmNu4BVQixppnCugRkeji0wNzEvsvzLL79C376vYGQErVrd+exTYmIidnZ2GBsbExkZSXh4OO7u7hV8FHqSoIQQogZQSpEaHYvxtWSumUNcAws8GzTHzNis2PVSUvTdy93cCn8wd/fu3cyZMwdTU1OMjIxYtmxZpU3cqSmlSlO+VIWFqG38/f05cOCAocMQVczJkydp1apVhW1fp9ORFhFF3WtXSLKEiw0s8bJvjqnx3bvjnT4NmZnQps3/394rT0Uce4nGqJAalBBCVGO5OTlkno6gbnoqCXUhxb4uze09MTG6+9f7jRuQkwONGlVMciorSVBCCFFNZWdkknsmHMusDOJtzUitb4GXrQfGRsYlWv/CBcjK0j/7VBVJghJCiGooM/UGWkQEZrnZRNiBUX0rPOu7YVTCqlBGBly5oq89GZcsn1U6SVBCCFHNpCWnYBYdiULHaXuoU78BrvVc0Uox/PiFC/pOEQ0bVmCgZSQJSgghqpHUhES0xIvkGCnC7RR29RvTxLpJqZJTVhYkJYGDQ9UZ1qgwVbBZTIjytW3bNlq0aIGnpyfz58+/Y3lmZiZDhw7F09OTjh07Eh0dDUBWVhZPPfUUPj4+tGvXjt8r+ulKIYqhlOJ6dAx1484BWZxy0OFo54KTjVOpkhPoJyRUqmrXnkASlKjhcnNzmTp1Kj///DMnTpxg/fr1nDhxokCZlStXYmtrS0REBC+88AIzZswAYMWKFQAcP36cHTt28NJLL6HT6Sr9GITQ6XTcOHMW68sXuWJpRFzjOrjYudGwbukzTE4OJCaCra1+5Ii7SUpKonv37tStW5dp06YVWHbw4EF8fHzw9PTkueeeo5SPLd2VJChRo4WGhuLp6Ym7uztmZmYMGzaMkJCQAmVCQkIYO3YsAIMGDWLnzp0opThx4gQ9evQAwNHRkfr168szTqLS5WRlk3niNHWvX+WCtRFRttDQujH2de6t611iIuTmQuPGJStvYWHB22+/zQcffHDHsilTprBixQrCw8MJDw9n27Zt9xRTUSRBiRotLi4OFxeX/PfOzs7ExcUVWcbExIR69eqRlJREu3bt+P7778nJySEqKoqDBw8SExNzxz6WL1+Ov78//v7+JCYmVuwBiVol80Y6uSdOYp5xg3O2RlyoZ0QLhxbUs6hX6m1FR0fTqlUrpk59muHDvRk4sOB0G0WxsrLi/vvvx+K26lZCQgLXrl2jU6dOaJrGmDFj2LJlS6njKo50khCiCOPHj+fkyZP4+/vTtGlTunTpgnEh/XGDgoIICgoCqJQBNEX199DXD921jC4nBy0jA4AME4XOyAhLU0uMtDvrFb+P+71E+w0PD2fWrPV8/fUKJk4sON3G7W6dbqMwcXFxODs7578v7MdfWUmCEjWak5NTgVpPbGwsTk5OhZZxdnYmJyeHlJQU7O3t0TSNjz76KL9cly5daN68eaXFLmqv3KwsjDMzyTUyIsNEh2ZkTB0Ty1J3hriVUuDk5Eb79r5YWxecbuOVV14px+jLjyQoUaMFBAQQHh5OVFQUTk5ObNiwgXXr1hUoExgYyKpVq+jcuTPBwcH06NEDTdNIS0tDKYWVlRU7duzAxMSE1q1bG+hIRE1SVI1HKUVq5Dmsr1zmhrkpZ+1ysa5ji2s91xKPDlGUlBQwMzOncWP980+3TrdxLzUoJycnYmNj898X9uOvrCRBiRrNxMSExYsX06dPH3Jzcxk/fjze3t7MmTMHf39/AgMDmTBhAqNHj8bT0xM7Ozs2bNgAwKVLl+jTpw9GRkY4OTmxZs0aAx+NqMlys3PIDD+Lddp1kuuaEWWdhb2VA671XAu9rVcaSum7lgPUr19w2SuvvHJPNajGjRtjY2PD3r176dixI6tXr+bZZ58tU5y3kwQlarx+/frRr1+/Ap/NnTs3/28LCws2bdp0x3rNmjXj9OnTFR6fEJlp6ajwCCyzM0mob0ZcnSycrJ1oVLdRmW7r3XRzSg0Tk8Kn1LibZs2ace3aNbKystiyZQvbt2+ndevWLF26lHHjxpGenk7fvn3p27dvmWO9lUy3IUQ5kuk2RGGKm24jLfkquXHx1MnK4LyDMcmmOTSr3+yeu5HfTik4dUr//JO3d+WPWi7TbQghRDWjlNLPfnshnmwTY844ahjXsaR53cZYm1uX236uX9dPq9G0adWcUqM4kqCEEKKS6XJ1pJ2NwvraFW5YmBNum4WxiRlu9VyxMCnB8A6lEB+vH2+vqk6pURxJUEIIUYmyMzLJiThL3Yw0km3qEGmVhrW5NR52HiWaZLA0rl+H1FRwcal+tSeQBCWEEJUm/ep1TKLOYq7LJd6hDvFmaTjUKZ+eeoVJSNB3jHBwKPdNVwpJUEIIUQlS4y+iJSaigKiG5mRbGOFkXn499W534wZcuwbOzlV3QsK7kQQlhBAVKDMtg8xLl6l74wZp5haEO2hkGmXhZuWEraVthe03IUGfmBo0qLBdVLhqeFdSCCGqh4vh0YS364R5+g1SbOpyyj6TXBONlg4tKzQ5paXB1av6+Z7KWnvasWMHfn5++Pj44Ofnx65du/KXyXQbQghRDR3bvAMVcB8e0ae4bm1BeN1U6phZ0cqhFXVM61TovhMS9J0iHB3Lvi0HBwd++OEHjh8/zqpVqxg9enT+MpluQwghqhGl0/HXC3NpOaQfp509eGFOR1JNdTjUcaC5fXNMjSt2jvX0dP3IEY6O+g4SN92cbuPpp5/G29ub3r1LNt1G+/btadKkCQDe3t6kp6eTmZkp020IIUR1cj05hZOBI7j/760c8unAKyMucygrivFmdWlar+n/d4Z46KHy3fHvv+f/mZCgf+6psOncw8PDWb9+PStWrGDIkNJPt7F582Y6dOiAubm5TLchhBDVxdm/D6MGD8Y/IZKtwwIZ4fMbpsbm/DrmV6zTrSukp97t0tMhORkaNdInqdu5ubnh6+sLlH66jbCwMGbMmMH27dvLO+wiSYISQogy2vfBcrxfn85RV2+2zh7MdONN+Nr78t3Q72havyknT54suMItNZ7ydLPtqbDaE4C5uXn+36WZbiM2NpbHH3+c1atX4+HhAch0G0IIUaVl3Ejn39FT6PjdKs40bck3L7nx6cVvGOkzkuUDlld4Z4hb3a32VJS7Tbdx9epVHn30UebPn0/Xrl3zP6+M6Takk4QQQtyD2GOniW4TgP93q/hnQCBPTNfxfeZ+FvVZxJrH11RqcgL9mHvF1Z7u1eLFi4mIiGDu3Ln4+vri6+vLpbzJpZYuXcrEiRPx9PTEw8NDptsQoiqT6TZqh9Dl6/GaPhnT3Bx+eHkkT1utw8rMim8GfcODzR68o3xx022Uh/R0CAvT155u6bdQJch0G0IIUQmy0jMJHT2V+zev5I8O3dk+oQnzElfQpVEXNg3eRBPrJgaJ62btqVEjg+y+wkiCEkKIEog7epq0QUO4P+IYe3oP4K3HL/PbxbU8d99zLOy9EDNjM4PElZYGV65A48YFn3uqCWrY4QghRPnb/+nXNJ/xLPV0On6YPZ0lzU+y7/xR1j2xjuE+w0u0DaVUhXQ1vznmXnm3PZWHsg59JJ0khBCiCBmpaewaHES7F57mcoMmLF42noEmn3Ih9QL7Ju4rcXKysLAgKSmp3Mequ1l7un3UiKpAKUVSUhIWFvc+AWMVOyQhhKgazv1ziOwhw+gRF86vwyfw8cPn+On8Ykb4jGDZo8tKNS27s7MzsbGxJCYmlmuMSUmQnQ2WlvqpNaoaCwuLAqNNlJpSqjQvIaqdn3/+WTVv3lx5eHio9957747lGRkZasiQIcrDw0Pdd999KioqSimlVFZWlhozZoxq06aNatmypZo3b95d9+Xn51fe4YtKpsvNVXtmf6BSTS3UNSsb9cO8mcrpQydl/ra5WrZ/mdLpdIYOUSmlVGioUqDU3LmGjuSelCjnSA1K1Gi5ublMnTqVHTt24OzsTEBAAIGBgbRu3Tq/zMqVK7G1tSUiIoINGzYwY8YMNm7cyKZNm8jMzOT48eOkpaXRunVrhg8fTrNmzQx3QKJCpVxI4swTI+m05xdONG/PD288xFfJm7FUluyZsIf2jdsbOsR8r7+unyl3+nRDR1JxpA1K1GihoaF4enri7u6OmZkZw4YNIyQkpECZkJAQxo4dC8CgQYPYuXNnfoP2jRs3yMnJIT09HTMzM2xsbAxxGKIShH37CycfeIT2e3fw59inmf6aLa+Gf8RDzR7iYNDBKpWcfvsNduyAmTPBuuR3GqsdSVCiRouLi8PFxSX/fWEjLt9axsTEhHr16pGUlMSgQYOwsrKicePGuLq68vLLL2NnZ3fHPpYvX46/vz/+/v7l3sYgKl5OZhYHJrxAi0H9qJdxne+XvsmT3lv4K24PKwas4PNHP8fGvOr8MFFKn5icnWHKFENHU7HkFp8QRQgNDcXY2Jj4+HiuXLnCAw88wMMPP4y7u3uBckFBQQQFBQH6kSRE9RF76ATXBg/DP/I4R7v1Zd2z7iwIm0Mbxzb8Puh3WjdoffeNVLIff4S9e2H5cihDB7lqQWpQokZzcnIiJiYm/31hIy7fWiYnJ4eUlBTs7e1Zt24djzzyCKampjg6OtK1a1cZxqiGUEqx593F1OsSgEvcWXbNmcPToy6zIGwJU/ynEDoxtEomJ51O3/bk6Qnjxhk6moonCUrUaAEBAYSHhxMVFUVWVhYbNmwgMDCwQJnAwEBWrVoFQHBwMD169EDTNFxdXdm1axcAN27cYO/evbRs2bLSj0GUr6sxFzjYuQ/1Pv6QWBdPNq+dzWzXXwlPDid4cDBLH12KpamlocMs1MaNcPw4zJ1buhHLqytJUKJGMzExYfHixfTp04dWrVoxZMgQvL29mTNnDt9//z0AEyZMICkpCU9PTxYtWsT8+fMBmDp1KqmpqXh7exMQEMBTTz1F27ZtDXk4ooyOrvyG7DZt8N2/i+T+/XjzbS+e+vc17OvYc2TSEZ5s/aShQyxSdjbMmQNt28LQoYaOpnLIaOZClCMZzbxqSrt6jaMjJ9N563rONWzKkYXTmXb5Qy6kXuCth95iRtcZGBsZGzrMYq1YAUFB8MMP0L+/oaMpMxnNXAghTv24izrjx9E5MYY9A0ayZaIDCw+/iKedJ3sm7MG/SdXv2JKRAW+9BZ07w6OPGjqayiMJSghRI2VnZBL6zGt4r19BprklO5d+wme2uwg5vJagDkEs6rMIKzMrQ4dZIqtWwY0bMG8eVMB4s1WWJCghRI0T+ftedKPH0jX2DDv7j+bwZA9mHf4PrYxa8e2Qb3m81eOGDrHErlyB116DBx+Ehx4ydDSVSxKUEKLGyMnMYv+01/H76mNSLazYNX8+bzn+xJ8H1jCw5UD+2/+/OFo5GjrMUpk/H65e1d/iq20kQQkhaoRz/xwiY+RoOkef4FBAD/a90YtXjr6N8UVjVg1cxei2oytkPqaKdP48fPIJjB4N7doZOprKJwlKCFGt5WbnsH/6HBxCgmmYfIHf5r7LQrc/+fnAa/R068mXj32Jaz1XQ4d5T+bM0f/37bcNG4ehSIISQlRb5/46QMaYcXSKCuPP+x/lj2WT+PDcSpIuJPFZ3894JuAZjLTq+bjnsWOwejW89BK4Vs/8WmaSoIQQ1U5OZhYHnptF+5Ufk25mwe9vzGWh5x62HnyZri5dCRkuvUq4AAAgAElEQVQWgpe9l6HDLJNXX4X69fUDw9ZWkqCEENVK1G97MXp6Ip3OhnHI7yH2v/EI/wmbR/a5bD7u8zHT7ptW5R+6vZtdu+Dnn2HhQrC1NXQ0hiMjSQhRjmQkiYqTlZbBwcn/wf7nEGwzUgl79SXec/md7VE7eLDpg6wMXImHnYehwywznQ7uuw8SE+H06Ro7YrmMJCGEqBlOh+zAfHIQnS9Ec6BLH3a91pP/HH8bXayOJf2WMNl/crVta7rd+vX6gWDnz6+xyanEasa/qBCiRkpLTmHvY2PwGtgHy/QbbP9gPtMnpDLl4H8Y6j2Uf5/5t1p3hLhderr+odysrNozIGxxpAYlhKiSjqzaTMMXp9Ep+QL/9BnM9inNmHdsNta51nz92NeMaTem2j3XdDeLFkFMDKxZA0Y1I+eWiSQoIUSVkhQVQ9ToSTTf/wfnmrgTOu8FXsv5mpNHNjHCZwQf9fmo2o0GURIXLsB778Hjj+uHNRKSoIQQVYTS6Tj45iI8P5hL28x09g0Zy/on4fOwGTSt15StI7bS16uvocOsMLNn62/tLVhg6EiqDklQQgiDi91zmGtPTcT/9CFOeLRl/5uDWXR9E+cizvFipxeZ231utRl5/F4cPQorV8ILL+incxd6kqCEEAaTmXqDg9Nm0jx4NbYql19efJEPfI7y69nZ+DX2Y9fYXXRo3MHQYVYopfSjRdjawqxZho6mapEEJYQwiLBVm7F5eTpdLsfya99h/DnKgfmRi7G8YMmSfkuY5Dep2j9wWxI//QQ7d8Knn9buh3ILIwlKCFGpksKjOD9uCu3/+YVYeyc2LnyNmWYbiQyPZFTbUSzstZBGdRsZOsxKkZUFn38OPXvC5MmGjqbqkQQlhKgUudk57H9tHt6L36dNbja7ho/j80eSCY56j5aWLdk1Zhfd3bobOsxK9cknsHWr/mVqauhoqh5JUEKICnd6y3aMn30WMCPKvRU/v9SF4Nw9hMWEMa/HPF7q8hJmxmaGDrNSJSTA3LnQvz/0rbmdE8tEHgUTNd62bdto0aIFnp6ezJ8//47lmZmZDB06FE9PTzp27Eh0dDQAa9euxdfXN/9lZGTEkSNHKjn66u1qdBz7H36CFo/3wSYliXOjuzFocgqvxn6GbyNfwp4J47UHXqt1yQn0o5VnZcFHHxk6kipMKVWalxDVSk5OjnJ3d1dnz55VmZmZqm3btiosLKxAmSVLlqhJkyYppZRav369GjJkyB3bOXbsmHJ3d7/r/vz8/Mon8GouJytbhc54V12vY62yjIzVzsAn1cDlvRVvolp81kL9HP6zoUM0qH/+UQqUevVVQ0diMCXKOVKDEjVaaGgonp6euLu7Y2ZmxrBhwwgJCSlQJiQkhLFjxwIwaNAgdu7cibptlP/169czbNiwSou7Ojv17TbCWgXQ4uN5xLh68O4no+gb8AO/Xv6Hhb0WcmzKMR7xfMTQYRqMTgfPPQdNmsDrrxs6mqpN2qBEjRYXF4eLi0v+e2dnZ/bt21dkGRMTE+rVq0dSUhIODg75ZTZu3HhHYhMFXQ6PImrCswT8+ROXbBz45sUhfOS0l/jUEIa1Gcb8nvNpbN3Y0GEa3Ndfw4ED8L//Qd26ho6mapMEJcRd7Nu3jzp16tCmTZtCly9fvpzly5cDkJiYWJmhVQnZ6RkcevFN2nz5Ke1ys9k2cADvPBTD31e/4j7z+9j22Fd0dO5o6DCrhKtX9W1PXbrAiBGGjqbqkwQlajQnJydiYmLy38fGxuLk5FRoGWdnZ3JyckhJScHe3j5/+YYNGxg+fHiR+wgKCiIoKAjQT1hYmxxfsZ70ZcvpeOh3DrT1579j7Pgi9Qeccp1Y8/gaRviMqDFTYZSHuXPh8mXYtg1q2EDsFUISlKjRAgICCA8PJyoqCicnJzZs2MC6desKlAkMDGTVqlV07tyZ4OBgevTokT+Ng06n45tvvuHPP/80RPhV1vm/D5Ay5Tl8ju8h0sWTD2c8zut1t2KUYcQbD77BK11eqdFj592LsDD47DN4+mnoULNHbyo3kqBEjWZiYsLixYvp06cPubm5jB8/Hm9vb+bMmYO/vz+BgYFMmDCB0aNH4+npiZ2dHRs2bMhff/fu3bi4uODu7m7Ao6g6UuIvcWryS/j9uI76ZpasGdmbV70P4dkoicH1B/Nez/dwtnE2dJhVjlL6gWAffhjeecfQ0VQf2u29le6iVIWFqG38/f05cOCAocModzmZWRyevQDPJQuxSU/l1wc7MrvXBfZnR9GtaTcWPryQ+5zvM3SYVda6dTBypH5YIxnSCIAS3eCUGpQQoljHv9iI0Ttv430xmlOuLrw/xIxvTPbQsl5LQh4OYUDzATVuZtvylJICL74IAQH623ui5CRBCSEKde73vVybNh2fsH2ct2/Ie5P8eM/2L+ytHPj8oc+Z2GEiJkbyFXI3s2bBpUv6UcuNa/7g7OVKri4hRAFJZ89xburLtNv+LdfNLflsaAdmtDiKZn6d+Q+9zyS/SVibWxs6zGrh4EFYuhSeeQb8/AwdTfUjCUoIAUD6lWscfXEO5r9uxyf+DFt6evP8fRFctDhGUIdJzH5wdq2ZBqM85ObClCnQoIF0jLhXkqCEqOVys7I5/OaHNPtsIZ1Sk/muszfzJrUnOPcAw9oM4+3ub+NpJ/OQl9YXX8D+/foRI+rXN3Q01ZMkKCFqKaXTcfy//8PxnTfwj4/mULMmjBlty88NwxjdejQHO/+3xk+3XlEuXoQ33oDu3WXEiLKQBCVELRT+/a/kvPQybSOOEuVgx7gx9qxyi6dbs2782eNd7ne939AhVmsvvQQ2NrBkiYwYURaSoISoRWL3HOLS8/+h4amjmOnSmfG4A4vaXMbXxZ9feqyjl3sv6TJeRr/8AmvXwpw50KqVoaOp3iRBCVELXD4RzvnnX6Xdzi3UNzVhYW8b/unbjgvaNTZ1X8FjLR6TxFQObtzQP4jbogXMnGnoaKo/SVBC1GDXYi5wcvpMfEP+hzc6Vna14fXOV3Fo6sCcbtMY0noIxkbycE55efNNiI6GP/4Ac3NDR1P9SYISogZKS7rC4ZnzabN6Kf6ZN/imQ11efeA6lh4N+eTBJQz1HiqJqZwdOgSLFulHi+jWzdDR1AySoISoQTKvp3J05nu0/HopXVOvsqqLMwt8U8lu2Yh3H1zK8DbDJTFVgJwcCAoCR0dYsMDQ0dQckqCEqAGy0zM4+sYHNF32EfddT2anpyWvdofUtnV5vdsahrUZJsMSVaBPP9WPGvHNN/LMU3mSK1aIaiw3K5sj732G6+IP8L+cwD+uZjz5JCQHuDOr2ywGtx4sNaYKFhmpH2dv0CD9S5QfSVBCVEO67ByOLFyGyYrP8Tl/in8bGTNqFCR2bc2sB2czsOVAmcm2EigFEyfqa09hYfLMU3mTBCVENaLLzuHfj7+g3gfz6HAphuOOxjw11paznT2Y/eAc+nn1k+7ilWjFCvjtN1i+HJxlnsZyV6oJCx955BF1+fLlMu80MTGRBg0alHk7lU3irlzVMe7jx4/j4+NT/htWkHbpMiYX4jHLySbdBOKtIdfGmsY2jbE2K9vo4tXxXINh487K0tearKygefPSrVvbz/fBgwd/UUo9cteCSqnSvMqFn59feW2qUknclas6xl2nTp1y3V5uVrY6vHCZ+qt1B6VAhTloasgg1MC1gWpf7L5y2091PNdKGS5unU6pvn2VqlNHqcjI0q8v57tkOUdu8QlRBemyczi6aDn1F72L76V4TjuYM2SwERaDh/PGQzNp3aC1oUOs1dasgZ9/hk8+ATc3Q0dTc0mCEqIKyc3K5siCpTh88i7tLyfybwMYOcQUl3HPsbDzVJrWb2roEGu9uDj46ivo2xemTTN0NDWbQRJUUFCQIXZbZhJ35aqOcTs4ONzTetnpGRycv5jGS9/D73IyRxvC7BF18Zz4Mp92nIZ9HftyjrSg6niuofLjVgomTIDQUDhyBIzusaOknO+SKVUnCaBUhYWobfz9/Tlw4ECJy2dcS+XQnPdo9vWnNElJ5ZvWGtvua0DA5DcY1+EpLE0tKzBaUVrLlulnyV2yRD+Nu7hnJepqKg9KiBpv27ZttGjRAk9PT+bPn3/H8szMTIYOHYqnpycdO3YkOjo6f9mxY8fo3Lkz3t7e+Pj4kJGRUS4xpV1O5o+Jz3C9iQNdPplHpE0qkyZ7YbH5O1asjGdKx2ckOVUxERH6eZ569dInKVEJStqbQpVjLz4hKktOTo5yd3dXZ8+eVZmZmapt27YqLCysQJklS5aoSZMmKaWUWr9+vRoyZIhSSqns7Gzl4+Ojjhw5opRS6vLlyyonJ6fY/d2tl1PK+QS1Y+hQddXSRClQ2zxQz8/oov4+9/e9HqKoBDk5SnXtqlS9ekrFxBg6mhqhRDmnwmpQb775Jk5OTvj6+uLr68vWrVsLLVfUr9uoqCg6duyIp6cnQ4cOJSsrq6JCLdSHH36IpmkU9tzXb7/9ln9cvr6+WFhYsGXLFgDGjRuHm5tb/rIjR45UmbgBjI2N82MLDAzM/9yQ57u4mI8cOZJfg2nbti0bN27MX1aScx0aGoqnpyfu7u6YmZkxbNgwQkJCCpQJCQlh7NixAAwaNIidO3eilGL79u20bduWdu3aAWBvb4+x8f8PG3S3c71q1Sq8vLzw8vLiiwUf81O/npzu5M7DGzfym6ui+6OOrOs/ho/e+4surl1Kf+JKafbs2bRt2xZfX1969+5NfHz8HWWq4rVdkrihYq/tDz+Ev//W39or6QO5JYm7rNd3RSjp+b71+l61alX+5wcPHsTHxwdPT0+ee+45VOmakQoqaSZTpaxBvfHGG2rhwoXFlinu1+3gwYPV+vXrlVJKTZo0SS1durQ0uy+T8+fPq969eytXV1eVmJhYbNmkpCRla2urbty4oZRSauzYsWrTpk2VEeYdShK3lZVVoZ8b6nzfLebTp0+rM2fOKKWUiouLU40aNVJXrlxRSpXsXG/atElNmDAh//3q1avV1KlTC5Tx9vZWMbf8LHZ3d1eJiYnqo48+UqNGjVK9e/dW7du3V++//36hcX/44YfKz89P+fn5KVdXV6WU/rpwc3NT+3/8Uf3Y2VtlGqGyNdRnXeqo7v3d1C9//KJ0Op165JFH1NatW0t51u5NSkpK/t+ffPJJfq2xKFXl2i5p3BV1bR89qpSZmVJPPql//qmkShJ3Wa/vilCSuG9e30lJSSo5OVm5ubmp5ORkpZRSAQEBas+ePXe7vg1bgyqJon7dKqXYtWsXg/JGXhw7dmz+r7jK8MILL7BgwYISDRkTHBxM3759qVOnTiVEVrzSxH0rQ57vu8XcvHlzvLy8AGjSpAmOjo4kJiZWSmw5OTn89ddfrF27lr/++ovvvvuOnTt33hH3mDFjOHDgAAcOHMh/yn7tgrdZbJpOh/796bE/jK/b2zDrjad47JtTxIeb0btb7/x1K+tc29jY5P9948aNu14nVeXaLm3ctyrrtZ2VBWPGgK0tfP556cbaK0nchry+i1KSuH/55Rd69eqFnZ0dtra29OrVi23btpGQkMC1a9fo1KlTuVzfFZqgFi9eTNu2bRk/fjxXrly5Y3lcXBwuLi75752dnYmLiyMpKYn69etjYmJS4PPKEBISgpOTU/5tnbvZsGEDw4cPL/DZ66+/Ttu2bXnhhRfIzMysiDDvUNK4MzIy8Pf3p1OnTvkXjqHOd2nPdWhoKFlZWXh4eOR/drdz7eTkRExMTP772NhYnJyciiyTk5NDSkoK9vb2ODs7061bNxwcHKhTpw79+vXj0KFDRcadm5vDlQtxBLdvwLPvf0zn85f48hEv9u3+kYuPvYyDVWsuJlzE+ZZ7RJV5bYP+fLm4uLB27Vrmzp1bbNmqcm3f3O/d4q6Ia/utt+DoUf2Ye/cywk9pzve9XN8V5W5xF/XdHRcXV77Xd0mrWqqQW3w9e/ZU3t7ed7y2bNmiLly4oHJyclRubq6aOXOmeuqpp+6o4xV1+yUxMVF5eHjkf37+/Hnl7e1daHX0XhQX93333aeuXr2qlFKqadOmxd7ii4+PVw4ODiorK6vAZzqdTmVkZKgxY8aot956q0rFHRsbq5RS6uzZs6pp06YqIiKiQs93eZ7r5s2bqz179hT47G7nOjs7W7m5uanIyMj828j//vtvgTKLFy8u0Eli8ODBqmfPnqply5bKwsJCtWrVSrVu3VpZWVmpWbNm3RH3qfAT6otnBqowR1PlB2qHm4la0NtbzZg5PX8fc+fOVQsXLlT79+9XPXv2zP989+7d6tFHH72HM1u44s73rebNm6fmzJlT5Haq0rVd0rjL+9r+5x+ljIyUuuUrqkLiVurer+97Vda4Fy5cqN5+++389/dwfZco51RKL76oqKhCL4p//vlH9e7dO//9vHnz1Lx585ROp1P29vYqOzu70HIV5dixY6pBgwaqadOmqmnTpsrY2Fi5uLiohISEQst//PHH6umnny5ye7/99lu5fvkUpbRx33TzHrchzndpYk5JSVHt27cv9n58cef6p59+Ul5eXsrd3V298847SimlZs+erUJCQpRSSqWnp6tBgwYpDw8PFRAQoM6ePZu/7po1a1Tr1q2Vt7e3euWVVwrE3bKtq5rZ3lHFWqMUqH8bmis3Rzt1/VqKWrdunQoKCsrfTlBQkFq3bp2Kj49XLVq0yP/89nKV5dy5c8V+UVeVa/t2d4v7prJe21evKuXmptTAgUrd0iRzz4qLu6zXd0UqKu5yuL4Nm6Di4+Pz/160aJEaOnToHWWK+3U7aNCgAg2bS5YsKc3uy8XdftV37NhR7dq1q8BnN49bp9Op559/Xs2YMaNCYyxMUXEnJyerjIwMpZRSiYmJytPTM79TiqHPd1ExZ2Zmqh49eqiPPvrojmWGONfZudnqf1s+Vl90a6R+cdcnpr88HdSPi95Rutzc/G7mSUlJqlmzZio5OVklJyerZs2aqaSkJKXUnY3IP/30U4XHrZTKb4xXSqlPP/1UPfnkk0WWrUrXdkniLs9rW6dTasQIpYyNlfq7DL3/SxJ3Vbu+lSpZ3OVwfRs2QY0aNUq1adNG+fj4qAEDBuSf7Li4ONW3b9/8coX9ulVKX00PCAhQHh4eatCgQfkXX2W69Utz//79BW5HRkVFqSZNmqjc3NwC63Tv3l21adNGeXt7q5EjR6rr169XasxKFR3333//rdq0aaPatm2r2rRpo7744ov8dQx9vouKec2aNcrExES1a9cu/3X48GGlVOWe6/hr8eq9BWNVcBtzla2hsoxQP3ZqqR5p3apA3A4ODvnrrFy5Unl4eCgPDw/15Zdf5n++f/9+5e3trdzd3dXUqVOVrjRdw8rgiSeeUN7e3srHx0f1798//5ZYVb+2SxJ3eV7bq1bpvxnnzq34uKvK9V3auJUq8/VdopwjQx0JUQSlFL+H72LPZ+/S9I/fGXlccdXcmL8f7k779z6liU+rO9Yp7VBHomoJD4cOHfSvXbvglsfeRPkqUX9IGc1ciNtczbjKV78tIWXpR4z7M4nuKfC7ZyN2TnmCzm+/w6P2toYOUVSArCwYPhxMTeF//5PkVBVIghIiz4H4A6za9A4t1v/IxMO5WGfBIQ9XLr/5Gt2mTsTIVP53qclmzYKDB+Hbb+GWHtTCgOT/OFGrXc+8ztpjazm9/mu6/7SP0Tc0fBNgf+cHaDL7bTr0edDQIYpKsH07LFwIkybB448bOhpxkyQoUSsdjD/Iij8+w2TDeqbsyWJyIly2suT0qEnceGU6XT1kYsDa4tIl/WgRrVvDokWGjkbcShKUqDVSMlJY/+96tm5dSs9tJ5l7JAc0U67auXL47Rdp82IQXevIFBe1iU6nrzU1bw6LF0MVGLFM3EISlKjRlFKExoXy+b6lJIdsYNLeLLaEQ66REae69qLOK6/QvP/DpRtkTdQY774LW7bA8uXQtq2hoxG3kwQlaqRLNy6x5uga1v+xjP5/JzPl8BU6XICrVjYcGjsWz9kv4SO38Wq1X3+FN96A0aNh4kRDRyMKIwlK1Bg5uhy2n91O8IlgwrauZlJoLn/+q2GZozjl6cOpj6bjHTSSBhbmhg5VGFhcHIwYoW93Ku0o5eLe7N+/nwkTJhAaGoqlpaUVEAoMVUr9W9Q6kqBEtReRHMGXh79kY+hXdNt3gUciTPgyLJcbZuac7D2QxjNeoGW3joYOU1QR2dkwbBikpcGmTWBlZeiIaoeAgAACAwOZNWsWwALgf8UlJ5AEJaqp65nX2XRiE18d/or0Y4cZuy+Dg4ehfiaca+zMkVcn0urlKXSwtzN0qKKKef11+OsvWLcOWt05GIioQHPmzCEgIADAH3jubuUlQYlqQ6d07I7ezepjqwk5spE+x9KY+a8Ffc9kkGVswqmufbj6wjSaPdaHpnLPRhQiJET/vNOUKfpRI0TlSkpKIjU1FcAasABuFFdexuITVd7Z5LOsPrqa1cdWYxEezQtHHRl08Ap26dn8064bdbp1xes/z2Ll3NjQocpYfFVYRAQMHQpGRvoalLk0RVa6wMBAhg0bxsiRI2cBjZVS04orLzUoUSWlZKQQfCKYHZE7CDmykf6nYe3+unQ5B9lGSZzu1JNrzz5DlyED9N84QhQjNVU/QkRysiQnQ1m9ejWmpqaMGDGCkSNHzgf+0TSth1JqV1HrSA1KVBk5uhx2nN3B6mOr2XJqCy1iMnjmiDVDj2SSZWRObn07Lg4agdcrU6nj4nT3DRqA1KCqHqVgyBD9GHvbtkGvXoaOSCCjmYvqQCnFkQtHWHd8HRvDNnLtYgxDwi3Zu9eCdvEZZBpncPr+3tR/djKuA/vSSIaYFqX0/vsQHAwLFkhyqm4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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画图：三次样条插值\n",
    "show_plot_range((-5, 5), hss, 'Cubic Spline Interpolation')\n",
    "show_plot_range((-5, -3), hss, 'Cubic Spline Interpolation')\n",
    "show_plot_range((-1, 1), hss, 'Cubic Spline Interpolation')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 拟合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalEquationFit(X, y):\n",
    "    \"\"\"最小二乘拟合\n",
    "    Compute the normal equations:\n",
    "\n",
    "    $\\theta = (X^TX)^{-1}X^Ty$\n",
    "\n",
    "    Args:\n",
    "        X: np.array, $$\n",
    "            X = \\left[\\begin{array}{c}\n",
    "            - (x^{(1)})^T - \\\\\n",
    "            - (x^{(2)})^T - \\\\\n",
    "            \\vdots \\\\\n",
    "            - (x^{(m)})^T - \\\\\n",
    "            \\end{array}\\right]\n",
    "        $$\n",
    "        y: np.array, $y = [y^{(1)},y^{(2)},\\dots,y^{(m)}]^T$\n",
    "\n",
    "    return theta.\n",
    "    \"\"\"\n",
    "    return np.dot(np.dot(np.linalg.pinv(np.dot(X.T, X)), X.T), y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "题目：3.4.2 数据拟合 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.45 1.25]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 2, 3, 4, 5])\n",
    "y = np.array([4, 4.5, 6, 8, 8.5])\n",
    "\n",
    "X = np.c_[np.ones((len(x), 1)), x]\n",
    "\n",
    "theta = normalEquationFit(X, y)\n",
    "print(theta)\n",
    "\n",
    "pred_f = lambda t: theta[0] + theta[1] * t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2501150707283306 2.449584558158982\n"
     ]
    }
   ],
   "source": [
    "# 用梯度下降检查\n",
    "\n",
    "a, b = 0, 0\n",
    "\n",
    "num_epoch = 10000\n",
    "learning_rate = 5e-4\n",
    "\n",
    "for e in range(num_epoch):\n",
    "    y_pred = a * x + b\n",
    "    \n",
    "    grad_a = 2 * (y_pred - y).dot(x)\n",
    "    grad_b = 2 * (y_pred - y).sum()\n",
    "    \n",
    "    a = a - learning_rate * grad_a\n",
    "    b = b - learning_rate * grad_b\n",
    "\n",
    "print(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
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\n",
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     "metadata": {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画图\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "pred_x = [k/10 for k in range(50)]\n",
    "pred_y = [pred_f(x) for x in pred_x]\n",
    "\n",
    "plt.plot(x, y, 'bo', label='date')\n",
    "plt.plot(pred_x, pred_y, 'r-', label='pred')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 题目：3.4.2 数据拟合 2.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([2, 3, 4, 7, 8, 10, 11, 14, 16, 18, 19])\n",
    "y = np.array([106.42, 108.2, 109.5, 110, 109.93, 110.49, 110.59, 110.6, 110.76, 111, 111.2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(1) $y(x) = c_0 + c_1x + c_2x^2$\n",
    "\n",
    "数据预处理："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  1.   2.   4.]\n",
      " [  1.   3.   9.]\n",
      " [  1.   4.  16.]\n",
      " [  1.   7.  49.]\n",
      " [  1.   8.  64.]\n",
      " [  1.  10. 100.]\n",
      " [  1.  11. 121.]\n",
      " [  1.  14. 196.]\n",
      " [  1.  16. 256.]\n",
      " [  1.  18. 324.]\n",
      " [  1.  19. 361.]]\n"
     ]
    }
   ],
   "source": [
    "# X: [1, x, x**2]\n",
    "X = np.c_[np.ones((len(x), 1)), x, x ** 2]\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义预测函数、代价函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hypothesis(x, theta):\n",
    "    return np.dot(theta, np.array([1, x, x**2]))\n",
    "\n",
    "def cost(x, y, hypothesis, theta):\n",
    "    return np.sum( (hypothesis(x, theta) - y) ** 2 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最小二乘正规方程拟合："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.06292705e+02,  6.26350752e-01, -2.04540298e-02])"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# theta: [c0, c1, c2]\n",
    "theta = normalEquationFit(X, y)\n",
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "计算代价："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.7796090121179953"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost(x, y, hypothesis, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可视化拟合："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "x_test = np.linspace(0, 25, num=100, endpoint=True)\n",
    "y_pred = hypothesis(x_test, theta)\n",
    "\n",
    "plt.plot(x, y, 'bo', label='date')\n",
    "plt.plot(x_test, y_pred, 'r-', label='pred')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(2) $y(x) = ae^{\\frac{b}{x}}$\n",
    "\n",
    "取对数：$\\ln(y) = \\ln(a) + \\frac{b}{x}$\n",
    "\n",
    "数据预处理："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.         0.5       ]\n",
      " [1.         0.33333333]\n",
      " [1.         0.25      ]\n",
      " [1.         0.14285714]\n",
      " [1.         0.125     ]\n",
      " [1.         0.1       ]\n",
      " [1.         0.09090909]\n",
      " [1.         0.07142857]\n",
      " [1.         0.0625    ]\n",
      " [1.         0.05555556]\n",
      " [1.         0.05263158]]\n"
     ]
    }
   ],
   "source": [
    "# X: [1, 1/x]\n",
    "X = np.c_[np.ones((len(x), 1)), 1 / x]\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "新的预测函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hypothesis(x, theta):\n",
    "    a, b = theta\n",
    "    h = np.exp(a) * np.exp(b / x)\n",
    "    return h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "拟合："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.7139705 , -0.09032026])"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# theta: [ln(a), b]\n",
    "theta = normalEquationFit(X, np.log(y))\n",
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "代价计算："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47193209161233546"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost(x, y, hypothesis, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
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    "x_test = np.linspace(0, 25, num=100, endpoint=True)\n",
    "y_pred = hypothesis(x_test, theta)\n",
    "\n",
    "plt.plot(x, y, 'bo', label='date')\n",
    "plt.plot(x_test, y_pred, 'r-', label='pred')\n",
    "plt.ylim(90, 120)\n",
    "plt.legend()\n",
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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